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Question

A and B can do a piece of work in 12 days , B and C can do a piece a work in 15 days while A and C can do a piece of work in 20 days. At what time C alone can complete the work ?


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Solution

A and B do a work in=12days

A and B do work in 1 day =112

B and C do a work in =15 days

B and C do a work in 1 day =115

A and C do a work in =20 days

A and C do a work in 1 day =120

So,

A+B=1121

B+C=1152

A+C=1203

By adding all these three equations we get,

A+B+B+C+A+C=112+115+120

2(A+B+C)=112+115+120=1×5+1×4+1×360=5+4+360=1260=15(A+B+C)=12×5=110

Now C work alone in one day

=(A+B+C)-(A+B)(onedaywork)=110-112=1×6-1×560=6-560=160

From here we say that C completes the work in 60 days.

Hence C completes the whole work alone in 60 days .


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